# View from the arXiv: Apr 18 - Apr 22 2022

A summary of new preprints appearing on arXiv during the week of Apr 18th to Apr 22nd 2022

Welcome to ‘View from the arXiv’, where each week I’ll put together a short list of new preprints which have appeared on arxiv.org during the week which I’ve found interesting. I’ll focus on the categories ‘*Disordered Systems and Neural Networks*’, ‘*Quantum Gases*’ and ‘*Strongly Correlated Electrons*’, and in particular the first two as these are the main areas of the arXiv which I follow. This is an entirely subjective list of things which appeal to me, and of course there are far too many interesting papers to be able cover all of them so I just choose one or two from each day to highlight here. As these are all preprints which have not yet been peer-reviewed, remember to take any claims and conclusions with a grain of salt and be sure to cast a critical eye over the work if you’re interested in more details. (And let’s face it, this caveat should be applied to any published work too…!)

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**Apr 18th**

*Due to the Easter weekend, there weren’t as many papers as usual out today and none of them caught my eye, so we’re skipping today…!*

**Apr 19th**

*Quantum critical behavior of entanglement in lattice bosons with cavity-mediated long-range interactions, by Shraddha Sharma, Simon B. Jaeger, Rebecca Kraus, Tommaso Roscilde, and Giovanna Morigi*: This is a super interesting work which looks at a Bose-Hubbard model in an optical cavity, which leads to an effective long-range interaction between bosons, which is mediated by the cavity photons. (In other words, the bosons talk to the photons, which then move around and talk to other bosons further away, as if the bosons talked directly to each other.) This gives rise to a long-range Bose-Hubbard model, which is super interesting and quite refreshing for anyone who’s mainly studied the (much more common!) short-range Bose-Hubbard model. This model hosts a variety of interesting phases of matter, including the Mott insulator and superfluid phases present in the short-range model, as well as additional charge density wave and supersolid phases that arise due to the long-range interactions. The phase diagram of this model has previous been mapped out using mean-field (Gutzwiller) methods, but the main object of interest in this paper is the entanglement, which the authors study using a so-called slave-boson approach. The authors demonstrate that the entanglement entropy is able to distinguish all phases (and phase transitions!) in the mode, which is a very cool result, and analyse in detail the various different phase transitions. One thing I’d love to know is whether these techniques could be applied to disordered systems, as the combination of long-range interactions and disorder brings us closer to the regime of interesting spin glass models. It looks to me that the analysis in this work makes use of momentum-space to simplify matters, which doesn’t usually provide much benefit in disordered systems, however I’m not entirely clear whether momentum space is required in order for the technique to work, or is just used here for convenience. Either way, it’s a very interesting paper that’s well worth a read!

*Many-body parametric resonances in the driven sine-Gordon model, by Izabella Lovas, Roberta Citro, Eugene Demler, Thierry Giamarchi, Michael Knap, and Edmond Orignac*: The Sine-Gordon model is an unusual quantum system that essentially consists of two one-dimensional Bose-Einstein condensates which are weakly coupled together, and it is host to some interesting and exotic physical effects. This work studies the Sine-Gordon model in the presence of periodic drive, where it’s known to exhibit a range of behaviours from a strong suppression of heating effects, through to states which quickly absorb energy from the drive and heat up. Periodic drives are usually easier to handle in the limit of high frequency drive, and so the low-frequency regime remains largely unexplored. Here, the authors aim to change that by studying how the Sine-Gordon model reacts to a slow, low-frequency drive, and in particular studies the different resonances present in the model, e.g the different frequencies at which the system is capable of absorbing energy from the periodic drive. The authors develop a semi-classical Truncated Wigner Approximation (TWA) which captures many of the features of the model and shines a light on the details of how the Sine-Gordon model reacts to drive, however it misses a few key aspects which the authors attribute towards true many-body effects which are beyond the scope of the TWA technique. This is quite a technical paper, but for anyone interested in how many-body systems respond to periodic drive, it’s a very interesting one.

**Apr 20th**

*Structural properties of local integrals of motion across the many-body localization transition via a fast and efficient method for their construction, by S. Adami, M. Amini, and M. Soltani*: Local integrals of motion play a key role in our understanding of many-body localisation, and it’s always interesting to see new methods designed to compute them. This work studies the many-body localisation transition through the lens of these integrals of motion (LIOMs, also known as *l*-bits), a difficult challenge as most methods which compute LIOMs work best in the localised phase but break down in the delocalised phase. The authors compute LIOMs here on relatively small system sizes, but in a manner that avoids this shortcoming and allows them to study the phase transition itself. (Though I note that this is something I’ve also worked on in the past, also using unitary transforms to compute LIOMs and study the phase transition.). They find that the phase transition appears to coincide with a percolation transition in Hilbert space. Very interestingly, the authors find that the MBL transition occurs at a *smaller* disorder strength than found in other words, which is at odds with recent arguments that the true MBL transition likely occurs at a much larger disorder strength than previously suspected. This could be due to the small system sizes studied here, or due to different methods being sensitive to different physical properties. I’m not entirely clear on the limitations of the method used in this work, so I’ll be interested to see how it develops in the future.

*The Coming Decades of Quantum Simulation, by Joana Fraxanet, Tymoteusz Salamon, and Maciej Lewenstein*: This is a chapter of an upcoming book titled *Sketches of Physics: The Celebration Collection*, and it’s a readable, accessible review of the modern quantum simulation landscape. It takes in quantum computing and the sorts of platforms likely to be used in the near future, then goes on to discuss what quantum simulation is, what it’s been used for in the past, and what more uses it could be put to in the future. It’s a long article that covers a lot of ground, so if you’re interested in a broad birds-eye view of what quantum simulation is and why it’s interesting, give this one a look.

**Apr 21st**

*The shared universality of charged black holes and the many many-body SYK model, by Jan Louw, and Stefan Kehrein*: Regular readers will know that I’ve featured several papers recently which study variations on the Sachdev-Ye-Kitaev model, an interesting model for the study of quantum chaos with deep connections to various gravitational theories. This work studies a novel modification to the SYK model, namely the case in which the number of operators in the interaction term is increased to some integer q/2 and the usual Majorana operators are replaced by more conventional Dirac fermions. By treating the parameter q as large, and therefore using 1/q as some small expansion coefficient, the authors of this work are able to obtain some remarkable insights into the properties of this modified SYK model. (This actually reminds me a bit of the random energy model studied in spin glasses, which is related to the more well-known p-spin glass model by taking p to infinity.) In particular, they show that the model exhibits a phase transition strongly reminiscent of that seen in charged black holes of Reissner-Nordström (RN) type. Not only that, but the transition seen in the SYK model turns out to be in the same universality class as the RN black hole theory. The authors also find a transition between chaotic and integrable phases, corresponding to a change between a zero-charge ground state that maps on to the Majorana SYK model and a charged Fermi gas. This is a step towards better connecting the charged SYK model with theories of gravity, and helping to establish what the gravitational dual of this model may be, deepening the connection between many-body quantum physics and black holes.

*Dynamical quantum phase transitions from quantum optics perspective, by Jakub Zakrzewski*: A 2-page paper with 11 references and a single author, in this day and age? This work stands out before we even get to the physics! The main aim of this short paper is to connect Rabi oscillations, an extensively studied property of two-level quantum systems, with a phenomenon called Loschmidt rate singularities, a hallmark of a dynamical quantum phase transition. The author starts with a simplified model, arguing that these two quantities are in fact tightly connected, before going on to make a case for this being a more general link that may be present in a variety of many-body systems, ending with a connection to quantum many-body scars. The latter connection seems a little tenuous to me at this stage, but appealling nonetheless. I’ll be curious to see whether the findings of this short paper stand up to scrutiny – as I’m far from an expert on these topics – or whether they are in the end chalked up to a cosmetic similarity or a coincidence. Either way, I suspect this short work will inspire quite a few longer ones in the near future.

**Apr 22nd**

*Mean field theory of failed thermalizing avalanches, by Philip J. D. Crowley, and Anushya Chandran*: First referenced as ‘upcoming’ a few weeks back in another paper about localisation in two-dimensional systems, I’ve been waiting with curiosity to read this. This work looks at the so-called ‘avalanche theory’ which attempts to describe the breakdown of many-body localisation due to the presence of rare regions in a system which locally thermalise. These regions grow with time as more and more lattice sites join the thermal bubble, eventually becoming large enough to thermalise the entire system and destroy localisation entirely. Using a new self-consistent entanglement mean-field theory, the authors of this work present results which suggest these thermal bubbles are unable to grow in two-dimensional systems with quasiperiodic potentials, meaning that they can only locally thermalise and can’t destroy localisation across the entire system. The key point is that thermalising events known resonances in quasiperiodic potentials are deterministic, and that the probability to encounter them does not depend on the specific ensemble realisation being considered (indeed, it depends only on properties of the quasiperiodic potential itself), in contrast to randomly disordered systems where in a large enough system there is *always* a chance of resonances which lead to the growth of thermal bubbles. Interestingly, this work studies a model of a system of local integrals of motion (LIOMs, or *l*-bits) coupled to an ergodic grain, rather than a microscopic model with a quasiperiodic potential. This could represent something of a worst case scenario for quasiperiodic systems, as the deterministic structure of resonances is unlikely to make these ergodic grains particularly common, and so being able to show that localisation is stable to their presence could have implications beyond isolated systems, but could also imply that 2D quasiperiodic systems might be stable towards the coupling with an external environment. All in all, this is quite an exciting work.